Mathematics, or math (sometimes also shortened as "maths"), is the study of numbers, shapes and patterns. Mathematicians are people whose job is to learn and discover such things in mathematics. The biggest part of mathematics is useful for solving problems that occur in the real world, so many people besides mathematicians study and use these parts of mathematics. Today in many kinds of jobs -- in business, science, engineering, and construction, for example -- knowledge about certain aspects of mathematics is needed. Mathematicians solve problems by using logic. Mathematicians often use deduction. Deduction is a special way of thinking to discover and prove new truths using old truths. To a mathematician, the reasons you know something is true are just as important as the fact that it is true. Using deduction is what makes mathematical thinking different from normal thinking. About Mathematics includes the study of:
Number: how many things there are.
Structure: how things are organized.
Place: where things are and their arrangement.
Change: how things become different over time.
Mathematics uses logic to study these things and to create general rules, which are an important part of mathematics. These rules leave out information that isn't important so that a single rule can cover many situations. By finding general rules, mathematics solves many problems at the same time. A proof gives a reason why a rule in mathematics is correct. This is done by using certain other rules that everyone agrees are correct, which are called axioms. A rule that has a proof is sometimes called a theorem. Experts in mathematics perform research to create new theorems. Sometimes experts find an idea that they think is a theorem but can not find a proof for it. That idea is called a conjecture until they find a proof. Sometimes, mathematics finds and studies rules or ideas that have not yet been found in the real world. Often in mathematics, ideas and rules are chosen because they are considered simple or beautiful. Sometimes these ideas and rules are found in the real world after they are studied in mathematics. This has happened many times in the past. This means that studying the rules and ideas of mathematics can help us know the world better. Number Mathematics includes the study of number, or quantity.
Natural numbers
Integers
Rational numbers
Real numbers
complex numbers
π,e
Arithmetic
Mathematical constant
Ordinal number
Cardinal number
Structure Some areas of mathematics study the structure that an object possesses.
Number theory
Abstract algebra
Linear algebra
Order theory
Graph theory
Operand theory
Place Some areas of mathematics study the arrangement of things.
Topology
Geometry
Trigonometry
Differential geometry
Fractal geometry
Change Ways to express and handle change in mathematical functions, at changes between numbers.
Calculus
Vector calculus
Analysis
Differential equations
Dynamical systems
Chaos theory
Applied mathematics Applied mathematics uses mathematics to solve problems of other areas such as engineering and physics. Numerical analysis – Optimization – Probability theory – Statistics – Mathematical finance – Game theory – Mathematical physics – Fluid dynamics Famous theorems These theorems have interested mathematicians and people who are not mathematicians. Pythagorean Theorem – Fermat's last theorem – Goldbach's conjecture – Twin Prime Conjecture – Gödel's incompleteness theorems – Poincaré conjecture – Cantor's diagonal argument – Four color theorem – Zorn's lemma – Euler's Identity – Church-Turing thesis These are theorems and conjectures that have greatly changed mathematics. Riemann hypothesis – Continuum hypothesis – P=NP – Pythagorean theorem – Central limit theorem – Fundamental theorem of calculus – Fundamental theorem of algebra – Fundamental theorem of arithmetic – Fundamental theorem of projective geometry – classification theorems of surfaces – Gauss-Bonnet theorem – Fermat's last theorem Foundations and methods Progress in understanding the nature of mathematics also influences the way mathematicians study their subject. Philosophy of mathematics – Mathematical intuitionism – Mathematical constructivism – Foundations of mathematics – Set theory – Symbolic logic – Model theory – Category theory – Logic – Reverse Mathematics – Table of mathematical symbols History and the world of mathematicians Mathematics in history, and the history of mathematics. History of mathematics – Timeline of mathematics – Mathematicians – Fields medal – Abel Prize – Millennium Prize Problems (Clay Math Prize) – International Mathematical Union – Mathematics competitions – Lateral thinking – Maths and gender Name The word "mathematics" comes from the Greek word "μάθημα" (máthema). The Greek word "μάθημα" means "science, knowledge, or learning". Often, the word "mathematics" is made shorter into maths (in British English) or math (in American English). The short words math or maths are often used for arithmetic, geometry or simple algebra by young students and their schools. Awards in mathematics There is no Nobel prize in mathematics. Mathematicians can receive the Abel prize and the Fields Medal for important works. The Clay Mathematics Institute have said they will give one million dollars to anyone who solves one of the Millennium Prize Problems Mathematical tools Tools that are used to do mathematics or find answers to mathematics problems. Old:
Mathematicians solve problems by using logic. Mathematicians often use deduction. Deduction is a special way of thinking to discover and prove new truths using old truths. To a mathematician, the reasons you know something is true are just as important as the fact that it is true. Using deduction is what makes mathematical thinking different from normal thinking.
About
Mathematics includes the study of:
- Number: how many things there are.
- Structure: how things are organized.
- Place: where things are and their arrangement.
- Change: how things become different over time.
Mathematics uses logic to study these things and to create general rules, which are an important part of mathematics. These rules leave out information that isn't important so that a single rule can cover many situations. By finding general rules, mathematics solves many problems at the same time.A proof gives a reason why a rule in mathematics is correct. This is done by using certain other rules that everyone agrees are correct, which are called axioms. A rule that has a proof is sometimes called a theorem. Experts in mathematics perform research to create new theorems. Sometimes experts find an idea that they think is a theorem but can not find a proof for it. That idea is called a conjecture until they find a proof.
Sometimes, mathematics finds and studies rules or ideas that have not yet been found in the real world. Often in mathematics, ideas and rules are chosen because they are considered simple or beautiful. Sometimes these ideas and rules are found in the real world after they are studied in mathematics. This has happened many times in the past. This means that studying the rules and ideas of mathematics can help us know the world better.
Number
Mathematics includes the study of number, or quantity.
Some areas of mathematics study the structure that an object possesses.
Some areas of mathematics study the arrangement of things.
Ways to express and handle change in mathematical functions, at changes between numbers.
Applied mathematics uses mathematics to solve problems of other areas such as engineering and physics.
Numerical analysis – Optimization – Probability theory – Statistics – Mathematical finance – Game theory – Mathematical physics – Fluid dynamics
Famous theorems
These theorems have interested mathematicians and people who are not mathematicians.
Pythagorean Theorem – Fermat's last theorem – Goldbach's conjecture – Twin Prime Conjecture – Gödel's incompleteness theorems – Poincaré conjecture – Cantor's diagonal argument – Four color theorem – Zorn's lemma – Euler's Identity – Church-Turing thesis
These are theorems and conjectures that have greatly changed mathematics.
Riemann hypothesis – Continuum hypothesis – P=NP – Pythagorean theorem – Central limit theorem – Fundamental theorem of calculus – Fundamental theorem of algebra – Fundamental theorem of arithmetic – Fundamental theorem of projective geometry – classification theorems of surfaces – Gauss-Bonnet theorem – Fermat's last theorem
Foundations and methods
Progress in understanding the nature of mathematics also influences the way mathematicians study their subject.
Philosophy of mathematics – Mathematical intuitionism – Mathematical constructivism – Foundations of mathematics – Set theory – Symbolic logic – Model theory – Category theory – Logic – Reverse Mathematics – Table of mathematical symbols
History and the world of mathematicians
Mathematics in history, and the history of mathematics.
History of mathematics – Timeline of mathematics – Mathematicians – Fields medal – Abel Prize – Millennium Prize Problems (Clay Math Prize) – International Mathematical Union – Mathematics competitions – Lateral thinking – Maths and gender
Name
The word "mathematics" comes from the Greek word "μάθημα" (máthema). The Greek word "μάθημα" means "science, knowledge, or learning".
Often, the word "mathematics" is made shorter into maths (in British English) or math (in American English). The short words math or maths are often used for arithmetic, geometry or simple algebra by young students and their schools.
Awards in mathematics
There is no Nobel prize in mathematics. Mathematicians can receive the Abel prize and the Fields Medal for important works.
The Clay Mathematics Institute have said they will give one million dollars to anyone who solves one of the Millennium Prize Problems
Mathematical tools
Tools that are used to do mathematics or find answers to mathematics problems.
Old:
- Abacus
- Napier's bones, slide rule
- Ruler and Compass
- Mental calculation
New: